## Abstract

The mean-square thermal displacements of the atoms in UO$_2$ and ThO~$_2$ have been determined as a function of temperature from the analysis of two-dimensional diffraction data. In the range investigated, 20 to 100$^\circ$C, the oxygen atoms vibrate more strongly than the metal atoms and at each temperature the displacements of the metal and oxygen atoms are slightly less in ThO$_2$ than in UO$_2$. The interpretation of these results gives a Debye characteristic temperature which is independent of temperature above 400$^\circ$C and equal to 377$^\circ$K for UO$_2$ and 393$^\circ$K for ThO$_2$. As the temperature roses, the oxygen atoms tend to be displaced from the fluorite-type sites at $\frac{1}{4}\frac{1}{4} \frac{1}{4}\ldots$~ towards the large interstitial holes at $\frac{1}{2}\frac{1}{2}\frac{1}{2}\ldots$ At~ 1000$^\circ$C the mean atomic co-ordinates of the oxygen atoms are ~$\frac{1}{4} + \delta \frac{1}{4} + \delta \frac{1}{4} + \delta \ldots~~$ where $\delta = 0\cdot016$ for UO$_2$ and ~$\delta = 0\cdot0.014$ for ThO$_2$. This relaxation effect indicates either that the oxygens are disordered or that they vibrate anharmonically across the ~$\frac{1}{4} \frac{1}{4} \frac{1}{4}\ldots$ positions.